Question 11

A small mass $m$ is in a circular orbit with radius $R$ about a central mass. The central mass is suddenly changed from $M$ to $M'=3M/4$ and the orbit of $m$ changes from a circle to an ellipse. Determine the semimajor axis $a$ and the eccentricity $e$ of the new orbit.

Describe what happens if the central mass is suddenly changed from $M$to $M/2$.

[Hints can be found here, but do not follow this link until you have attempted the question on your own.]